Park City Mathematics Institute
Reasoning from Data and Chance
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- Data Explorations using World Cup Data
- Andy Katz* and Douglas Lutz
- Every four years the world pauses to celebrate the most popular sport and ultimate tournament, the FIFA World Cup. Over two hundred teams compete to be among the 32 qualifiers to the quadrennial Cup. These two explorations are intended to scaffold student understanding of statistics and promote statistical literacy using Fathom Dynamic Data and 2010 World Cup Data. These are based on the 2005 Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report, endorsed by the American Statistical Association and follows the suggested progression of understandings fundamental to learning data analysis and statistics. The first exploration focuses on distributions of goals scored and yellow cards given. Students are asked to summarize and compare distributions graphically and numerically, and make conclusions based on shape and centers, in the proper context. The second exploration introduces students to the idea of association between two quantitative variables (shots and goals scored) and presents dot plots as a graphical display for investigating such association. It also presents the correlation coefficient as a numerical summary of association between two quantitative variables.
- What's Your Statistic? Using Coin Tosses to Generate and Use an Unfamiliar Sampling Distribution
- Jane Kang and Vicki Lyons*
- This lesson is designed to give students experience with generating a sampling distribution. Students will invent their own test statistic for measuring randomness of a coin toss. They will use this statistic to generate a sampling distribution using Fathom. Then, given both randomly and non-randomly generated coin toss sequences, students will develop a more authentic understanding of p-values as they examine the likelihood of each sample statistic when compared to their sampling distribution. Students can then discuss the reasonableness and reliability of their test statistic to measure randomness. By having students use unconventional test statistics, this lesson pushes students to a deeper understanding of sampling distributions, p-values, and making conclusions.
- Exploring Relationships in the 2010 Census
- Carol Kinney*, Amanda Morgan, Chance Nalley
- Students will work with prepared graphs created from 2000 US Census data (drawn from Louisville, KY, New York, NY, and Philadelphia, PA). Students will be presented with visual displays showing the relationships between given variables such as educational attainment, personal income, race, gender, etc., and asked to theorize missing variables through reasoning. Students will use the process of elimination, sort variables into categorical versus quantitative variables and think about the possible outcomes or sample space for two variables. Using group discourse and teacher facilitated classroom discussion, students will consider how aspects of social context, such as age and geographical location, create predictable shapes in data representations. Students will verify their conclusions by using Fathom software to explore, recreate, and analyze the data set while continuously drawing comparisons between their work and the given data representations.
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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.